How to get NURBS control points from an array of points that should be part of its solution from controll points we are searching for?

Question

We are talking about Non-uniform rational B-spline. We have some simple 3 dimensional array like

{1,1,1}
{1,2,3}
{1,3,3}
{2,4,5}
{2,5,6}
{4,4,4}

Which are points from a plane created by some B-spline

How to find control points of spline that created that plane? (I know its a hard task because of weights that need to be calculated but I really hope it is solvable)